MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Rank of a Matrix

The rank of t...

Question

The rank of the matrix $⎡ ⎢ ⎣ \begin{matrix} - 4 & 1 & - 1 - 1 & - 1 & - 1 7 & - 3 & 1 \end{matrix} ⎤ ⎥ ⎦$ is

A

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

C

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 2
A = $⎡ ⎢ ⎣ \begin{matrix} - 4 & 1 & - 1 - 1 & - 1 & - 1 7 & - 3 & 1 \end{matrix} ⎤ ⎥ ⎦$
$R_{2} \leftrightarrow R_{1} \to ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 1 & - 1 - 4 & 1 & - 1 7 & - 3 & 1 \end{matrix} ⎤ ⎥ ⎦$

$\begin{matrix} R_{2} \to R_{2} - 4 R_{1} R_{3} \to R_{3} + 7 R_{1} \end{matrix}} T h e n A \sim ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 1 & - 1 0 & 5 & 3 0 & - 10 & - 6 \end{matrix} ⎤ ⎥ ⎦$

$R_{3} \to R_{3} + 2 R_{2} T h e n A \sim ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 1 & - 1 0 & 5 & 3 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦$

Hence $ρ (A) = Number of non zero rows = 2$

Suggest Corrections

thumbs-up

0

Similar questions

Q. The rank of the matrix

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & - 2 & - 1 - 3 & 3 & 0 2 & 2 & 4 \end{matrix} ⎤ ⎥ ⎦

Q. The rank of the matrix

⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 1 & - 1 & 0 1 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦

Q. The rank of the matrix

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 1 & - 1 & 0 & 0 & 0 0 & 0 & 1 & - 1 & 0 0 & 1 & - 1 & 0 & 0 - 1 & 0 & 0 & 0 & 1 0 & 0 & 0 & 1 & - 1 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

Q. Find the rank of matrix :

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 1 & 1 & 1 1 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦

Q. Find the value of: (1-1/3 )(1-1/4)( 1-1/5) _____?_____ 1-1/n

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Solving Linear Equation

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Rank of a Matrix

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon